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lfunc_lfunctions • Show schema
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{'Lhash': '2116849084158317286826302018330', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [0.0, 0.0], 'a5': [-0.7071067811865476, 0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [-0.7071067811865476, -0.7071067811865476], 'a8': [0.0, 0.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6768584424468882, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [7, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '3360.3233', 'coefficient_field': 'CDF', 'conductor': 3360, 'conductor_radical': 210, 'conjugate': '649897572386135194332231611381', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0.7071067811865476, 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[0, -1.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-3360-105.83-c0-0-6', 'leading_term': '0.97386534408388945813236069103361', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3360/1/bn/b/3233/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.9738653440838895, 1.0625454635675933, 1.159054898444824, 1.264532400430304, 1.3793647426655717, 1.50320123284768, 1.6350241587454928, 1.7732473339993613, 1.9158202021754214, 2.060324367079107, 2.204057868837114, 2.3441079286546436, 2.4774153564651265, 2.6008343181628866, 2.711190638984615, 2.8053409130577456, 2.88023373578686, 2.9329735206521583, 2.9608866474477096, 2.961589112936664, 2.9330544014472326, 2.8736799457212863, 2.7823502950681176, 2.6584949408972913, 2.5021386650118793, 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'6.80896370279099142041000967866821', '8.035267091361205260211748305195000', '8.382692510544872679309752573399045', '8.788480309901355348589718034492594'], 'prelabel': '2-3360-105.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2949356904676341, 'root_angle': 0.6762081911747834, 'root_number': '-0.52573111211913360602566908484825 + 0.85065080835203993218154049706283*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3381040955873917', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66989948474539997603693503365', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81701798163101577554049097297', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65805592110341863055821231420', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6768584424468882, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.83', 'conductor': 3360, 'conductor_radical': 210, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3360/1/bn/b/3233/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-3360-105.83-c0-0-6', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3360-105.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2949356904676341, 'root_angle': 0.3381040955873917, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.66989948474539997603693503365', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2116849084158317286826302018330', 'Lhash_array': ['2116849084158317286826302018330'], 'label': '2-3360-105.83-c0-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3360/1/bn/b/3233/2'}